Nonlinear viscoelastic constitutive model for bovine liver tissue

Soft tissue mechanical characterisation is important in many areas of medical research. Examples span from surgery training, device design and testing, sudden injury and disease diagnosis. The liver is of particular interest, as it is the most commonly injured organ in frontal and side motor vehicle crashes, and also assessed for inflammation and fibrosis in chronic liver diseases. Hence, an extensive rheological characterisation of liver tissue would contribute to advancements in these areas, which are dependent upon underlying biomechanical models. The aim of this paper is to define a liver constitutive equation that is able to characterise the nonlinear viscoelastic behaviour of liver tissue under a range of deformations and frequencies. The tissue response to large amplitude oscillatory shear (1–50%) under varying preloads (1–20%) and frequencies (0.5–2 Hz) is modelled using viscoelastic-adapted forms of the Mooney–Rivlin, Ogden and exponential models. These models are fit to the data using classical or modified objective norms. The results show that all three models are suitable for capturing the initial nonlinear regime, with the latter two being capable of capturing, simultaneously, the whole deformation range tested. The work presented here provides a comprehensive analysis across several material models and norms, leading to an identifiable constitutive equation that describes the nonlinear viscoelastic behaviour of the liver.

     

Paediatric brain tissue properties measured with magnetic resonance elastography

Biomechanics and Modeling in Mechanobiology - The aim of this study is to characterise the stiffness of white and grey matter in paediatric subjects using magnetic resonance elastography (MRE) and...     

Unconfined compression of white matter

The porous properties of brain tissue are important for understanding normal and abnormal cerebrospinal fluid flow in the brain. In this study, a poroviscoelastic model was fitted to the stress relaxation response of white matter in unconfined compression performed under a range of low strain rates. A set of experiments was also performed on the tissue samples using a no-slip boundary condition. Results from these experiments demonstrated that the rheological response of the white matter is primarily governed by the intrinsic viscoelastic properties of the solid phase. The permeability of white matter was found to be of the order of 10(-12) m4/Ns.     

Models of the pulsatile hydrodynamics of cerebrospinal fluid flow in the normal and abnormal intracranial system

Images obtained from magnetic resonance imaging have helped to ascertain that both the cerebrospinal fluid (CSF) and brain move in a pulsatile manner within the cranium. However, these images are not able to reveal any quantitative information on the physiological forces that are associated with pulsatile motion. Understanding both the pressure and velocity flow field of CSF in the ventricles is important to help understand the mechanics of hydrocephalus. Four separate fluid structure interaction models of the ventricular system in the sagittal plane were created for this purpose. The first model was of a normal brain. The second and third models were pathological brain models with aqueductal stenosis at various locations along the fluid pathway. The fourth model was of a hydrocephalic brain. Results revealed the hydrodynamics of CSF pulsatile flow in the ventricles of these models. Most importantly, it has also revealed the different changes in CSF pulsatile hydrodynamics caused by the various locations of fluid flow obstructions.     

Stress relaxation of human ankles is only minimally affected by knee and ankle angle

Comprehensive characterization of stress relaxation in musculotendinous structures is needed to create robust models of viscoelastic behavior. The commonly used quasi-linear viscoelastic (QLV) theory requires that the relaxation response be independent of tissue strain (length). This study aims to characterize stress relaxation in the musculotendinous and ligamentous structures crossing the human ankle (ankle-only structures and the gastrocnemius muscle–tendon unit, which crosses the ankle and knee), and to determine whether stress relaxation is independent of the length of these structures. Two experiments were conducted on 8 healthy subjects. The first experiment compared stress relaxation over 10 min at different gastrocnemius muscle–tendon unit lengths keeping the length of ankle-joint only structures fixed. The second experiment compared stress relaxation at different lengths of ankle-joint only structures keeping gastrocnemius muscle–tendon unit length fixed. Stress relaxation data were fitted with a two-term exponential function (T=G₀+G₁e^?λ₁t+G₂e^?λ₂t). The first experiment demonstrated a significant effect of gastrocnemius muscle–tendon unit length on G₁, and the second experiment demonstrated an effect of the length of ankle-joint only structures on G₂, λ₁ and λ₂ (p<0.05). Nonetheless, the size of effects on stress relaxation was small (ΔG/G<10%), similar to experimental variability. We conclude that stress relaxation in the relaxed human ankle is minimally affected by changing gastrocnemius muscle–tendon unit length or by changing the lengths of ankle-joint only structures. Consequently quasi-linear viscoelastic models of the relaxed human ankle can use a common stress relaxation modulus at different knee and ankle angles with minimal error.     

The presence of arachnoiditis affects the characteristics of CSF flow in the spinal subarachnoid space: a modelling study

Syringomyelia is a neurological disorder characterised by high pressure fluid-filled cysts within the spinal cord. As syringomyelia is associated with abnormalities of the central nervous system that obstruct cerebrospinal fluid (CSF) flow, it is thought that changes in CSF dynamics play an important role in its pathogenesis. Using three-dimensional computational models of the spinal subarachnoid space (SAS), this study aims to determine SAS obstructions, such as arachnoiditis, change in CSF dynamics in the SAS. The geometry of the SAS was reconstructed from a series of MRI images. CSF is modelled as an incompressible Newtonian fluid with a dynamic viscosity of 1 mPa s. Three computational models simulated CSF flow in either the unobstructed SAS, or with the SAS obstructed by a porous region simulating dorsal or circumferential arachnoiditis. The permeability of this porous obstruction was varied for the model with dorsal arachnoiditis. The results show that arachnoiditis increases flow resistance in the SAS and this is accompanied by a modest increase in magnitude and/or shift in timing (with respect to the cardiac cycle) of the CSF pressure drop across the region of arachnoiditis. This study suggests that syrinx formation may be related to a change in temporal CSF pulse pressure dynamics.     

Viscoelastic properties of human cerebellum using magnetic resonance elastography

BackgroundThe cerebellum has never been mechanically characterised, despite its physiological importance in the control of motion and the clinical prevalence of cerebellar pathologies. The aim of this study was to measure the linear viscoelastic properties of the cerebellum in human volunteers using Magnetic Resonance Elastography (MRE).MethodsCoronal plane brain 3D MRE data was performed on eight healthy adult volunteers, at 80 Hz, to compare the properties of cerebral and cerebellar tissues. The linear viscoelastic storage (G′) and loss moduli (G″) were estimated from the MRE wave images by solving the wave equation for propagation through an isotropic linear viscoelastic solid. Contributions of the compressional wave were removed via application of the curl-operator.ResultsThe storage modulus for the cerebellum was found to be significantly lower than that for the cerebrum, for both white and grey matter. Cerebrum: white matter (mean±SD) G′=2.41±0.23 kPa, grey matter G′=2.34±0.22 kPa; cerebellum: white matter, G′=1.85±0.18 kPa, grey matter G′=1.77±0.24 kPa; cerebrum vs cerebellum, p<0.001. For the viscous behaviour, there were differences in between regions and also by tissue type, with the white matter being more viscous than grey matter and the cerebrum more viscous than the cerebellum. Cerebrum: white matter G″=1.21±0.21 kPa, grey matter G″=1.11±0.03 kPa; cerebellum: white matter G″=1.1±0.23 kPa, grey matter G″=0.94±0.17 kPa.DiscussionThese data represent the first available data on the viscoelastic properties of cerebellum, which suggest that the cerebellum is less physically stiff than the cerebrum, possibly leading to a different response to mechanical loading. These data will be useful for modelling of the cerebellum for a range of purposes.     

Large deformation shear properties of liver tissue

Characterization of the mechanical properties of soft biological tissues is important for establishing the mechanical tolerances of the tissues, and for input to computational models. In this work, the viscoelastic properties of bovine liver tissue in shear loading have been measured using relaxation and constant shear rate loading. The tissue is nonlinearly viscoelastic for strains greater than 0.2%, has a yield strain of approximately 10, and shows moderate strain-rate sensitivity. The response can be modelled using a nonlinear viscoelastic differential model previously developed for brain tissue.     

Arterial pulsation-driven cerebrospinal fluid flow in the perivascular space: a computational model

This study was conducted to determine whether local arterial pulsations are sufficient to cause cerebrospinal fluid (CSF) flow along perivascular spaces (PVS) within the spinal cord. A theoretical model of the perivascular space surrounding a "typical" small artery was analysed using computational fluid dynamics. Systolic pulsations were modelled as travelling waves on the arterial wall. The effects of wave geometry and variable pressure conditions on fluid flow were investigated. Arterial pulsations induce fluid movement in the PVS in the direction of arterial wave travel. Perivascular flow continues even in the presence of adverse pressure gradients of a few kilopascals. Flow rates are greater with increasing pulse wave velocities and arterial deformation, as both an absolute amplitude and as a proportion of the PVS. The model suggests that arterial pulsations are sufficient to cause fluid flow in the perivascular space even against modest adverse pressure gradients. Local increases in flow in this perivascular pumping mechanism or reduction in outflow may be important in the etiology of syringomyelia.     

Large strain behaviour of brain tissue in shear: some experimental data and differential constitutive model.

In this paper, some experimental measurements of the behaviour of bovine brain tissue under large shear strains in vitro are reported, and a constitutive model which is consistent with the data is developed. It was determined that brain tissue is not strain-time separable, showing slower relaxation at higher strains, and that the stresses in shear are not linear with increasing shear strain. The new constitutive model is a differential model, including both an "elastic" term, of the Mooney type and a nonlinear viscoelastic term. The latter allows for the change in relaxation behaviour with strain, by modifying an upper convected multimode Maxwell model with a damping function. The model shows good agreement with the experimental shear results and could be used to describe other types of data.